22/21: Difference between revisions

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{{Infobox Interval

| Name = small undecimal semitone

| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second

| Color name = 1or1, loru unison

| Sound = jid_22_21_pluck_adu_dr220.mp3

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}}

'''22/21''' is a small [[superparticular]] ~~'''~~semitone~~'''~~ of about 80.5¢ that appears in [[11-limit]] [[just intonation]]. It makes the difference between the 21st and 22nd [[harmonic]]s~~. It is close in size to [[21/20]], a 7-limit superparticular interval, differing from it by [[441/440]], about 3.9¢~~.

'''22/21''' is a small [[superparticular]] [[semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s.

~~The single degree of~~ [[~~88cET~~]] ~~can function~~ as ~~both 21~~/20 and 22/21, ~~thus tempering out 441~~/~~440~~.

In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. However, it is only flat of the [[256/243|Pythagorean minor second (256/243)]] by a [[896/891|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.

Further more, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.

== Approximation ==

10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = small undecimal semitone
+| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second
 | Color name = 1or1, loru unison
 | Sound = jid_22_21_pluck_adu_dr220.mp3
@@ Line 6: / Line 6: @@
 }}
-'''22/21''' is a small [[superparticular]] '''semitone''' of about 80.5¢ that appears in [[11-limit]] [[just intonation]]. It makes the difference between the 21st and 22nd [[harmonic]]s. It is close in size to [[21/20]], a 7-limit superparticular interval, differing from it by [[441/440]], about 3.9¢.
+'''22/21''' is a small [[superparticular]] [[semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s.
-The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.
+In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. However, it is only flat of the [[256/243|Pythagorean minor second (256/243)]] by a [[896/891|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.
+Further more, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.
+== Approximation ==
 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.